Abstract: To control the normal acceleration in a corner area for machining, a quintic Pythagorean-Hodograph (PH) curve is introduced for corner smoothing. The normal acceleration as well as the velocity of the trajectory is controlled. Parameters for constructing the PH curves are proposed according to the situation of the corner. S-shape velocity profile is used to ensure the speed in line and circle machining. The velocity based on the rate of curvature is presented to meet the shape of the corner. The jerk of the S-shape acceleration is modified at the start and the end of the corner for the connection of speed. The federate in the corner area is controlled by the constraint of acceleration and chord error. The results show that the replacement error of the PH curve in the corner is less than 7.4 μm，which is sufficient to satisfy the requirements for machining. Meanwhile the difference of the normal acceleration is suppressed. A smooth velocity profile is obtained by the connection of the S-shape for the trajectory and the curvature based on the corner.

Key words: computer numerical control, corner smoothing, Pythagorean-Hodograph curve, S-shape velocity profile, errors